Dynamics of films and droplets spreading on porous substrates

摘要

This paper investigates numerically spreading and sorption of films and droplets on an unsaturated porous substrate, as taking place e.g. in the process of ink jet printing. The dynamics of the fluid on the substrate surface is treated in the framework of lubrication approximation. Fluid flow within the porous substrate, caused by the droplet penetrating into it, is treated in the framework of Richards' equation, which models unsaturated flow in porous media. Numerical results are presented for sorption of an axisymmetric droplet into a substrate of finite thickness, showing the influence of the sorption characteristics of the porous material on the final fluid distribution within the substrate. The approach taken here goes beyond conventional wetting front models in that it allows to describe fluid transport in the porous layer after complete absorption of the liquid above the substrate surface. Both the absorption kinetics of the film or droplet and the final fluid distribution in the substrate are relevant for evaluating the efficiency and the quality of coating and printing processes.